You have this solution to Maxwell's equations in vacuum: $$\widetilde{\mathbf{E}}(x,y,z,t) = \widetilde{\mathbf{E}}_0 \exp\left[i\left(\mathbf{k}\cdot\mathbf{r} - \omega t\right)\right]$$ If this wave travels in the $y$ direction, is polarized in the $x$ direction, and has a complex phase of 0, what is the $x$ component of the physical wave? 1. $E_x = E_0 \ cos\left(kx-\omega t\right)$ 2. $E_x = E_0 \ cos\left(ky-\omega t\right)$ 3. $E_x = E_0 \ cos\left(kz-\omega t\right)$ 4. $E_x = E_0 \ cos\left(k_x x+k_y y-\omega t\right)$ 5. Something else Note: * Correct Answer: B

The electric fields of two EM waves in vacuum are both described by: $$\mathbf{E} = E_0 \sin(kx-\omega t)\hat{y}$$ The "wave number" $k$ of wave 1 is larger than that of wave 2, $k_1 > k_2$. Which wave has the larger frequency $f$? 1. Wave 1 2. Wave 2 3. impossible to tell Note: * Correct Answer: A * Same speed and thus wavelength of 1 is smaller, so frequency is higher